Melbourne's strategy of a back five, with Mark Milligan effectively man-marking Heskey, appeared successful with the former Liverpool front man limited in the first half.
However, a cross from Josh Brillante and a Ruben Zadkovich corner laid the platform for Heskey's goals in the 54th and 56th minutes.
The Jets held on for their third straight win despite Archie Thompson pulling a goal back late on.
The visitors handed new signing Nathan Coe a spot in goal, replacing Tando Velaphi, while Jonathan Bru started in place of the injured Gui Finkler.
For Newcastle, there was some surprise when James Virgili, who was lively in last week's win against Central Coast, was relegated to the bench in place of Ben Kantarovski.
Taylor Regan missed out for Brillante.
Melbourne started sharply with Marco Rojas forcing a save from Mark Birighitti inside two minutes.
The lively Rojas was back in the action in the 19th minute when he combined with Marcos Flores but was unable to find Thompson for the opener.
After 25 minutes, the Jets had their first significant chance.
Kantarovski had a good run blocked by Melbourne skipper Adrian Leijer just outside the penalty area.
Leijer was cautioned for the tackle, but Zadkovich was unable to make the most of the chance, curling his free-kick just past the post.
Victory looked the more dangerous of the two sides in the first half with Rojas, Thompson and Adama Traore all having good chances.
Newcastle started the better in the second half and had opportunities, notably to Ryan Griffiths, before 34-year-old Heskey's quick double.
A deflected Brillante cross fell into Heskey's path and the striker made no mistake with his finish to make it 1-0.
He doubled his team's advantage just two minutes later when, after a scramble in the area, he was left unmarked to hook an effort over his shoulder and past a helpless Coe.
Thompson gave Victory a chance to get back into the match in the 71st minute when a failed Tiago Calvano clearance fell to the Socceroo, who nodded into the bottom corner.
Seven minutes later, Thompson miscued a cross from substitute Theo Markelis as Ange Postecoglou's side failed to find a leveller.